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The domain of the function $f (x) = \log_{1 / 2} (x - \frac{1}{2}) + \log_{2} \sqrt{4 x^{2} - 4 x + 5} is$

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12,∞

(−∞,∞)

None of these

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Correct option is B

log1/2⁡x−12 is defined if x−12>0 i.e., x>12 log2⁡4x2−4x+5 is defined if 4x2−4x+5>0⇒4x−122+1>0 which is true for all real x.∴ Domain of f=12,∞.

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The domain of the function f(x)=log1/2⁡x−12+log2⁡4x2−4x+5 is

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The domain of the function $f (x) = \log_{1 / 2} (x - \frac{1}{2}) + \log_{2} \sqrt{4 x^{2} - 4 x + 5} is$